DRAFT
Proposal for a general methodology for compatibility
analysis of aeronautical radio systems including the
determination of frequency and distance separation for
radio systems
Introduction
The purpose of this contribution is to describe a general methodology, which can be used
in interference analysis for different radio systems. This proposal is mainly based on
ITU-R Recommendation SM.337-4 which is an attempt to logically combine currently
available models and parameters of both desired and undesired systems, e.g. signal power
and spectral distribution, receiver selectivity, antenna patterns, propagation attenuation
etc. For example, interference problems can be created by the power from an emission in
one band overlapping into an adjacent band and interacting with a receiver tuned close to
the band edge.
The following primary factors, which quantify the interactive effects between interfering
transmitters and victim receivers for various frequency or distance separations are:
-
the frequency dependent rejection (FDR) which is a measure of the rejection
produced by a receiver selectivity curve on an unwanted transmitter emission, and
-
frequency / distance (FD) which is a measure of the minimum distance separation
that is required between a victim receiver and an interfering transmitter as a function
of difference between their tuned frequencies.
The frequency/distance rules are an important part of the frequency management process
in most radio services. In channelized services, these rules take the following form: cochannel transmitters must be separated by at least d0 (NM), the adjacent channel
transmitters must be separated by at least d1 (NM), transmitters separated by two
channels must be at least d2 (NM) away and so on. The introduction of new technologies
raises the question: what kind of FD rules should be applied when different systems
occupy the same frequency band?
FD and FDR can provide solutions of co- and adjacent channel frequency sharing and
adjacent band interference problems by providing estimates of minimum required
frequency and geographic separation between interfering transmitters and victim
receivers which are required for an adequate receiver performance.
Note: Throughout this document, capital letters are used to denote logarithmic values
(dB) of the corresponding quantities designated with lower-case type, e.g. PD = 10 log pD.
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PD is the input power to the transmitting antenna (dB) relative to 1 W when pD is the
input power (W).
Methodology
The electromagnetic compatibility of radio equipment should be calculated by the
following method:
1.
2.
3.
determine the desired signal level at the victim receiver front end;
determine the resulting level of interference at the victim receiver’s front end;
determine the interactive effects among wanted signals, interference and receiver
characteristics for various frequency or distance separations;
determine the appropriate ITU-R propagation model to be used; and
determine, from these data, a relationship between the frequency separation and
distance separation that the interference is considered tolerable.
4.
5.
Procedure
A compatibility analysis between an undesired transmitter and a victim receiver can be as
follows:
Step 1: Determine the desired signal level PD (dBW) at the victim receiver front end.
PD  PTx _ D  GTx _ D ( )  LTx _ D _ FL  GRx ( D )  LRx _ FL  LPOL _ Rx _ D  Lb (d D )
(1)
where:
PD :
desired signal level PD (dBW) at the victim receiver front end
PTx_D :
output power of the desired transmitter (dBW)
GTx_D():
gain of the desired transmitting antenna in direction of victim receiver with respect to an
isotropic antenna (dBi)
LTX_D_FL :
feeder link losses between output of the desired transmitter and the input of the desired
transmitting antenna (dB)
GRx(D) :
gain of the receiving antenna in direction of desired transmitter with respect to an
isotropic antenna (dBi)
LRX_FL :
feeder link losses between output of the receiving antenna and the input receiver (dB)
LPOL_Rx_D :
loss due to polarization mismatch of receiving antenna with respect to desired transmitted
signal (dB)
Lb (dD ) :
basic transmission loss for a separation distance dD between desired transmitter and
receiver (dB) (see Recommendation ITU-R P.341)
:
angle between boresight of transmitting antenna and receiving antenna
D
angle between boresight of receiving antenna and desired transmitting antenna
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As an alternative approach the desired signal power level PD (dBW) at the victim receiver
front end can be determined based on the minimum required field strength within the
service volume.
PD  E  20  log f  107.2  GRx ( D )  LRx _ FL  LPOL _ Rx _ D
(1a)
where:
E:
minimum required electric field strength at the edge of the service area (dB(V/m))
f:
frequency (MHz)
GRx(D) :
gain of the receiving antenna in direction of desired transmitter with respect to an
isotropic antenna (dBi)
LRX_FL :
feeder link losses between output of the receiving antenna and the receiver input (dB)
LPOL_Rx_D :
loss due to polarization mismatch of receiving antenna with respect to desired transmitted
signal (dB)
D
angle between boresight of receiving antenna and desired transmitting antenna
Note: When assuming the minimum field strength throughout the service volume than
this approach is slightly more conservative since it does not take into account actual field
strength values.
Step 2: Calculate the resulting level of interference at the victim receiver’s front end
using the formula:
PU  PTx _ U  LTx _ U _ FL  GTx _ U ( )  GRx ( U )  LRx _ FL  LPOL _ Rx _ U  Lb (dU )  FDR (f )
where:
PU :
undesired signal level PU (dBW) at the victim receiver front end
PTx_U :
output power of the undesired transmitter (dBW)
LTX_U_FL :
feeder link losses between output of the undesired transmitter and the input of the
undesired transmitting antenna (dB)
GTx_U():
gain of the undesired transmitting antenna in direction of victim receiver with respect to
an isotropic antenna (dBi)
GRx(U) :
gain of the receiving antenna in direction of undesired transmitter with respect to an
isotropic antenna (dBi)
LRX_FL :
feeder link losses between output of the receiving antenna and the input receiver (dB)
LPOL_Rx_U :
loss due to polarization mismatch of receiving antenna with respect to undesired
transmitted signal (dB)
Lb (dU ) :
basic transmission loss for a separation distance dU between undesired transmitter and
receiver (dB) (see Recommendation ITU-R P.341)
FDR (f ) :
frequency depended rejection for a frequency separation f as expressed by equation (3)
:
angle between boresight of transmitting antenna and receiving antenna
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(2)
U
angle between boresight of receiving antenna and undesired transmitting antenna
FDR is the rejection provided by a receiver to a transmitted signal as a result of the
limited bandwidth of the receiver with respect to the transmitted signal and the detuning
between the receiver and the transmitter.

FDR(f )=10 log 
 p( f )df
0
dB
(3)
 p( f ) h( f )df
0
where:
p( f ) :
power spectral density of the interfering signal (W/Hz); and
h( f ) :
normalized frequency response of the receiver.
f  f Rx  f Tx _ U
(4)
where:
fRx :
receiver tuned frequency; and
fTx_U :
interferer tuned frequency.
The FDR can be divided into two terms, the on-tune rejection (OTR) and the offfrequency rejection (OFR). The OTR is the rejection provided by a receiver selectivity
characteristic to a co-tuned transmitter as a result of a transmitted signal exceeding the
receiver bandwidth. The OFR is an additional rejection that results from off-tuning
between interferer and receiver.
Note: FDR, OTR and OFR are considered as losses and defined below in a manner to
ensure positive values.
fdr (f )  otr  ofr (f )
(5)
And in logarithmic values:
FDR (f )  OTR  OFR (f )
dB
(6)
where:
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
 p( f )df
OTR 10 log 
0
dB
(7)
 p( f ) h( f  f ) df
0

OFR(f ) 10 log
 p( f ) h( f  f )df
0
dB

(8)
 p( f ) h( f )df
0
The on-tune rejection also called the bandwidth correction factor can often be
approximated by:
B 
OTR  K  log  T 
 BR 
BR  BT
(9)
where:
BR : interfered receiver 3 dB bandwidth (Hz)
BT : interferer transmitter 3 dB bandwidth (Hz)
K  10 for non-coherent signals
K  20 for pulse signals.
Note: OTR = 0
if BR  BT
Step 3: The interference will be considered tolerable if the following inequality is
satisfied:
PD  PU    ASF
(10)
where:
PD :
desired signal level PD (dBW) at the victim receiver front end
PU :
undesired signal level PU (dBW) at the victim receiver front end

protection ratio (dB)
ASF
aviation safety factor (dB)
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In some cases it is required to calculate the interference-to-noise ratio (I/N) at the IF
output or demodulation input of the victim receiver. The interference will be considered
tolerable if the following inequality is satisfied:
I  I 
    ASF
N  N  req
(11)
where:
I/N :
calculated interference-to-noise ration at the victim receiver input referred to the IF
bandwidth (dB)
(I/N)req :
required interference-to-noise ration at the victim receiver input referred to the IF
bandwidth (dB)
ASF
aviation safety factor (dB)
The noise at the receiver input referred to the IF bandwidth is given by:
N  10  log k  T0  10  log BIF  NF
(12)
where:
N:
receiver noise power (dBm)
k:
Boltzmann’s constant
T0
absolute temperature (K)
BIF
receiver’s intermediate frequency bandwidth (Hz)
NF
receiver noise figure (dB)
The I/N ratio is then given by:
I
 PU  10  log k  T0  10  log BIF  NF
N
(13)
Step 4: Determine the appropriate ITU-R propagation model to be used
See Annex 1 for propagation models.
Step 5: Determine a relationship between the frequency separation and distance
separation that the interference is considered tolerable
The maximum acceptable value of undesired signal power at the victim receiver front end
can be derived by rearranging of equation 10.
PU _ max  PD    ASF
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where:
PD :
desired signal level PD (dBW) at the victim receiver front end
PU_max :
maximum acceptable undesired signal level P U (dBW) at the victim receiver front end

protection ratio (dB)
ASF
aviation safety factor (dB)
When the maximum acceptable value of undesired signal power from an interferer is
specified, equation 2 is rearranged to give the required propagation loss.
Lb (dU )  FDR(f )  PTx _ U  LTx _ U _ FL  GTx _ U ( )  GRx (U )  LRx _ FL
 LPOL _ Rx _ U  PU _ max
(15)
Substitute PU_max of step 5 above into equation (15) to derive or numerically compute a
relationship between the frequency separation  f and the distance separation dU such that
the interference is considered tolerable.
Lb (dU )  FDR(f )  PTx _ U  LTx _ U _ FL  GTx _ U ( )  GRx (U )  LRx _ FL
 LPOL _ Rx _ U  PD    ASF
(16)
The required loss combines a distance dependent term Lb(dU) and a frequency dependent
term FDR(f).
Using equation 16 an FD plot can be developed showing various combinations of the two
separations in frequency f and in distance dU, which achieves the required loss between
the desired and the undesired signals.
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Annex 1
Propagation Models
Free – Space Propagation Model
1
The propagation loss that would occur if the antennas were replaced by isotropic
antennas located in a perfectly dielectric, homogeneous, isotropic and unlimited
environment, the distance between the antennas being retained (see Recommendation
ITU-R P.525).
 4   d 
Lbf  20  log 

  
(A1-1)
where:
Lbf :
free-space basic transmission loss (dB)
d:
distance
:
wavelength, and
d and  are expressed in the same unit.
Equation (A1-1) can also be written using the frequency instead of the wavelength.
Lbf  32.4  20  log f  20  log d
(A1-2)
where:
f:
frequency (MHz)
d:
distance (km).
or
Lbf  37.8  20  log f  20  log d
(A1-3)
where:
f:
frequency (MHz)
d:
distance (NM)
2
Aeronautical Standard Propagation Model
Aeronautical standard propagation model (ASPM) is derived from the ITU-R
Recommendation P.528. For distances up to the radio horizon, free space propagation is
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assumed. Beyond the radio horizon, a constant attenuation factor a, which depends on the
frequency band under consideration, is used.
The distance to the radio horizon can be calculated using the following formula.
d RH  2  k  RE 

hTx  hRx

(A1-3)
where:
dRH :
distance to the radio horizon
k:
effective Earth radius factor
RE
Earth radius
hTX
height of transmitting antenna above Earth’s surface
hRX
height of receiving antenna above Earth’s surface
Tx
Rx
hTx
hRx
dRH
k·RE
If heights hTX and hRX are expressed in Feet (ft) an the distance d in Nautical Miles (NM),
the Earth radius RE = 6360 km and if the atmospheric conditions are assumed to be
normal (effective Earth radius factor k = 4/3) the following practical formula can be used:
d RH  1.23 

hTx  hRx

(A1-4)
where:
dRH :
distance to the radio horizon (NM)
hTX
height of transmitting antenna above Earth’s surface (ft)
hRX
height of receiving antenna above Earth’s surface (ft)
The propagation loss between two isotropic antennas located in a perfectly dielectric,
homogeneous, isotropic and unlimited environment can be calculated as follows:
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Lbf (d ) 
37.8  20  log d  20  log f
if d  d RH
a(d  d RH )  L(d RH )
if d  d RH
(A1-5)
where:
Lbf(d) :
transmission loss between transmitter and receiver as a function of distance (dB)
d:
distance between transmitter and receiver (NM)
dRH :
distance to the radio horizon (NM)
f:
frequency (MHz)
d:
distance (NM)
a:
constant attenuation factor beyond radio horizon (dB/NM)
In the band 108 – 137 MHz: a = 0.5 dB/NM
In the band 960 – 1215 MHz: a = 1.6 dB/NM
In the band 5030 – 5091 MHz: a = 2.7 dB/NM
L(dRH) :
free space transmission loss for the distance up to radio horizon (dB)
Tx
hTx
Rx
hRx
dRH
d
k·RE
Note: The constant attenuation factors a were derived from ITU-R Recommendation
P.528 for 125 MHz, 1200 MHz and 5100 MHz for 50 % of the time.
3
Two-Ray Propagation Model
t.b.d.
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